New Trends in Information Technologies - Kettering...

Krassimir Markov Vitalii Velychko

Lius Fernando de Mingo Lopez Juan Casellanos (editors)

New Trends in

Information Technologies

I T H E A SOFIA

2010

Krassimir Markov Vitalii Velychko Lius Fernando de Mingo Lopez Juan Casellanos (ed)

New Trends in Information Technologies

ITHEAreg

Sofia Bulgaria 2010

ISBN 978-954-16-0044-9

First edition

Recommended for publication by The Scientific Concil of the Institute of Information Theories and Applications FOI ITHEA

This book maintains articles on actual problems of research and application of information technologies especially the new approaches models algorithms and methods of membrane computing and transition P systems decision support systems discrete mathematics problems of the interdisciplinary knowledge domain including informatics computer science control theory and IT applications information security disaster risk assessment based on heterogeneous information (from satellites and in-situ data and modelling data) timely and reliable detection estimation and forecast of risk factors and on this basis on timely elimination of the causes of abnormal situations before failures and other undesirable consequences occur models of mind cognizers computer virtual reality virtual laboratories for computer-aided design open social info-educational platforms multimedia digital libraries and digital collections representing the European cultural and historical heritage recognition of the similarities in architectures and power profiles of different types of arrays adaptation of methods developed for one on others and component sharing when several arrays are embedded in the same system and mutually operated It is represented that book articles will be interesting for experts in the field of information technologies as well as for practical users

General Sponsor Consortium FOI Bulgaria (wwwfoibgcom)

Printed in Bulgaria

Copyright copy 2010 All rights reserved

copy 2010 ITHEAreg ndash Publisher Sofia 1000 POB 775 Bulgaria wwwitheaorg e-mail infofoibgcom

copy 2010 Krassimir Markov Vitalii Velychko Lius Fernando de Mingo Lopez Juan Casellanos ndash Editors

copy 2010 Ina Markova ndash Technical editor

copy 2010 For all authors in the book

reg ITHEA is a registered trade mark of FOI-COMMERCE Co

ISBN 978-954-16-0044-9

Co Jusautor Sofia 2010

I T H E A

134

CALCULATING OF RELIABILITY PARAMETERS OF MICROELECTRONIC COMPONENTS AND DEVICES BY MEANS OF VIRTUAL LABORATORY

Oleksandr Palagin Peter Stanchev Volodymyr Romanov Krassimir Markov Igor Galelyuka Vitalii Velychko Oleksandra Kovyriova

Oksana Galelyuka Iliya Mitov Krassimira Ivanova

Abstract Today together with actual designing and tests it is often used virtual methods of designing which support prior calculations of parameters of the developed devices Such parameters include reliability For this purpose the virtual laboratory for computer-aided design which is developed during joint project by VM Glushkov Institute of Cybernetics of NAS of Ukraine and Institute of Mathematics and Informatics of BAS contains program unit for calculating reliability parameters of separate microelectronic components and whole devices The program unit work is based on two computing method the first one uses exponential distribution of failure probability and the second one ndash DN-distribution of failure probability Presence of theoretical materials computing methods description and other background materials lets to use this program unit not only for designing and scientific researches but also in education process

Keywords Virtual Laboratory Computer-Aided Design Reliability Calculation Distributed System

ACM Classification Keywords J6 Computer-Aided Engineering ndash Computer-Aided Design (CAD) K43 Organizational Impacts ndash Computer-Supported Collaborative Work

Introduction

Modern microelectronic component base lets to develop portable devices for wide and everyday using on the base of effects and phenomena which exist in medicine biology biochemistry etc Actual design of new devices and systems which is often used needs a lot of time material and human resources These expenses may be reduced with help of virtual methods of designing which are realized by means of virtual laboratories of computer-aided design (VLCAD) [Palagin 2009]

VLCAD is worth to be used on the stage of the requirements specification or EFT-stage because it gives the possibility enough fast to estimate the project realization certain characteristics and as a result expected benefit of its practical realization Using of VLCAD doesn`t need expensive actual tests and complicated equipments

Calculating of parameters

Devices what are developed are generally data acquisition and processing channels During designing and modeling such systems (channels) it is very important to make prior parameters calculating and evaluating These parameters include reliability precision performance cost etc

Having only model of future device it is possible enough quickly to make prior calculating of device parameters Also we have possibility to calculate several alternative variants of project and choose the optimal one according to user criteria (or predetermined criteria) For prior calculating we developed and filled databases which contain information about a large amount of microelectronic components and units Databases contain next main parameters 1) microelectronic component name 2) manufacturer of microelectronic component 3) group to which microelectronic component belongs 4) parameters which are intrinsic to some group of microelectronic components eg nominal currents voltages and powers interface types 5) manufacturing technique


135

6) reliability parameters 7) work temperature range 8) price 9) body type and conditions of installing 10) unique properties of microelectronic component

For prior calculating of each parameter it is developed program model Under program model we mean separate program group of programs or program complex which let by means of calculating sequence and graphical display of result to reproduce processes of object functioning under influence of as a rule random (or predetermined) factors The model purpose is to obtain quantitative or qualitative results Quantitative result is intended to predict some future values or explain some past values which characterized whole systems Qualitative results on the base of analysis let to detect some earlier unknown system characteristics

Generalized graphical display of stages sequence of prior calculating is shown on the fig 1 (portable device Floratest [Romanov 2007] is as example)

Fig 1 Sequence of stages of prior parameter calculating of developed devices

Calculating of reliability

Most devices are generally data acquisition and processing channels Such channels are per se systems without recovery elements of which are connected serially But meaning series connection doesnt always agree with physical series connection [Belyaev 1985] In this case we mean that failure of any system element causes failure of whole device or channel

Because of complexity of physical processes which cause failures impossibility to take account of all start conditions and random influences in present days it is accepted to consider a failure as random event in meaning that if we even know structure type of system and application conditions it is impossible to detect time and place of failure

I T H E A

136

As a rule prior evaluation of reliability parameters of separate microelectronic components is made by manufacturers on the base of results of highly accelerated stress tests [MIL-STD-883] Reliability parameters are shown in general form and grouped by types of manufacturing technique or large classes of functional-similar components (amplifiers converters processors controllers memory etc) Reliability level of modern microelectronic components is estimated by next characteristics

1) failure rate which measured in units FIT (failure in 109 hours of work)

2) mean time to failure Т0

Mean time to failure is estimated as function of failure rate in consideration of distribution law of failure probability Today there are many computing methods of reliability which are based on different distribution laws of failure probability [Azarskov 2004] We analyzed methods which are oriented on computer and instrumentation tools and adapted them for realization as program models

For prior calculating of reliability parameters of components devices and systems it is created program unit for calculating of reliability parameters This program unit has next features

1) calculating reliability parameters of separate microelectronic component or whole device

2) using different computing methods which are based different distribution laws of failure probability

3) selecting for calculating reliability parameters of device both component experimental data which are got by manufacturers with help of accelerated tests and component data which calculated by program unit

4) comparing of reliability parameters calculating results which were obtained by means of different computing methods

5) optimizing reliability index on the base of microelectronic components from VLCAD databases

6) containing fundamentals about reliability theory including computing sequence of reliability parameters by means of every computing method

The work of program unit for calculating reliability parameters of microelectronic components and whole devices is based on using two computing methods which are adapted by us for realization as program models

1) by using exponential law of distribution of failure probability (probabilistic model of failure distribution) which is used by many manufacturers of microelectronic components

2) by using DN-distribution of failure probability (probabilistic-physical model of failure distribution) which was proposed by Ukrainian scientists V Strelnikov and O Feduhin [Azarskov 2004 Streljnikov 2004]

Selected models of distribution have very important difference Probabilistic model allows only two state of system elements ndash operable and faulty Probabilistic-physical model considers continuous set of system element and system states with continuous time First model uses exponential law of distribution of failure probability the second one ndash DN-distribution

As was written above the exponential law of distribution of failure probability is used by many manufacturers of microelectronic components such as Analog Devices Inc [ADI 2004] Motorola [Motorola 1996] etc This law of distribution is recommended by Department of Defense of USA [MIL-STD-883] Exponential law is one-parametric function

According to this method failure rate is got from experimental data of manufacturer or calculated by formula

2

2

AtHN

(1)

where χ2 ndash function values of which depend on component failure quantity and confidence bounds of interval and are received from [Romanov 2003 Motorola 1996] N ndash quantity of components under accelerated tests H ndash


137

duration of accelerated tests hours At ndash coefficient of failure rate acceleration which is calculated by the formula [Streljnikov 2002] (Arrhenius law)

11

rv TTk

Ea

eAt (2)

where Еа ndash activation energy (= 07 еV) k ndash Boltzmann constant (=861710-5) Тv ndash temperature of accelerated tests К Тr ndash work temperature of microelectronic component К

Mean time to failure Т0 in accordance with exponential law is calculated by formula

1

0 T (3)

For calculating mean time to failure Тсре (exponential law) of whole device it is used the next formula

1

1

n

jjj

еср mT (4)

where mj ndash quantity of units of j type (j = 1 2hellip n) λj ndash failure rate of units of j type

For calculating reliability parameters by means of second adapted method it is used DN-distribution of failure probability which is two-parametric function as opposed to exponential law In [Azarskov 2004 Streljnikov 2004] it is shown that by using DN-distribution it is possible to get result which are more close to real data

For calculating reliability parameters of microelectronic components by means of DN-distribution it was updated and adapted algorithm which is shown in [Azarskov 2004] It will be shown on the example the features of every method For this it is necessary to calculate mean time of test of every sample by formula

N

EDHtн (5)

where EDH ndash parameter equivalent device hours which can be found in the manufacturer documentation manufacturer web-site or calculated by formula

AtHNEDH (6)

Mean time to failure Т0 is calculated by substitution of values λ and tн in formula (λ can be calculated by (1) or found in the manufacturer documentation)

)(

)(

н

н

tR

tf (7)

where

2

exp2

)(0

200

н

н

ннн tT

Tt

tt

Ttf

(8)

)2exp()(0

0

0

0

н

н

н

нн

tT

TtФ

tT

tTФtR (9)

Since during experimental evaluation of failure rate of microelectronic components the rate of microelectronic components with failures is 1hellip5 [Streljnikov 2004] so it is possible to consider λ asymp f(tн) So the formula (7) can be written as

2exp

2 0

200

н

н

нн tT

Tt

tt

T

(10)

For calculating mean time to failure ТсрD (DN-distribution) of whole device it is used next formula

I T H E A

138

2

1

1

2

n

jjj

Dср TmT (11)

Computing algorithms of reliability parameters by means of these two methods are shown on fig 2 Program unit which is developed by authors is a part of VLCAD and operates on the base of these computing algorithms

Fig 2 Computing algorithms of reliability parameters with using of exponential law of distribution of failure probability (а) and DN-distribution of failure probability (b)

Using developed program unit it were obtained dependences of system operating reliability versus time For simplifying it is considered that system consists of same microelectronic components that are manufactured by means of same manufacturing technique (eg Bipolar lt 25 μm2) Should note that program unit allows to calculate reliability parameters of systems which consist of different quantities of microelectronic components manufactured by means of different manufacturing technique Dependences were obtained for 4 systems which consist of 1 thousand 10 thousand 20 thousand and 100 thousand microelectronic components respectively Confidence bounds equal 60 Dependences obtained by means of method on the base of exponential law of distribution of failure probability are shown on fig 3 and fig 4 Dependences obtained by means of method on the base of DN-distribution of failure probability are shown on fig 5


139

Fig 3 Dependence of probability of system operating reliability (1 000 and 10 000 components) versus time exponential law of distribution of failure probability


I T H E A

140

Fig 5 Dependence of probability of system operating reliability (1 000 10 000 20 000 and 100 000 components) versus time DN-distribution of failure probability

Combine some calculated values to the table for more detail analysis of obtained dependences (table 1) For more visualization the table data are used for plotting graphic (fig 6) Should note that as in previous cases system consists of same microelectronic components that are manufactured by means of same manufacturing technique Bipolar lt 25 μm2

Table 1 Duration of no-failure operation of systems which consist of different quantities of components

Quantities of micro-electronic components

T0 Exponential law of distribution DN-distribution

CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141

CB = Confidence bounds

It was analyzed systems which consist of from 1 thousand to 200 thousand microelectronic components Such range of components wasnt selected by accident On this range according to our analysis it is happened some changes in ratio of reliability parameters which were calculated by two methods

Fig 6 Dependence of duration of no-failure operation of systems which consist of different quantities of components versus quantities of system components

Having analyzed graphics (fig 3ndash6) and table 1 it is possible to make next conclusions For every confidence bound (in our case there are 60 and 90 ) there is such system components quantity below of which the method on basis of exponential law of distribution overstates the reliability parameters and above of which ndash puts too low them For confidence bound 60 this quantity equals approximately 60 thousand components and for confidence bound 90 ndash respectively 20 thousand The difference of results that are obtained by means of these two computing methods can be explained by method error [[Streljnikov 2004] The method error becomes apparent because exponential law of distribution is one-parametric function while DN-distribution is two-parametric function or in other words diffusive distribution

Our conclusion conforms very well with test and computing results which were fulfilled by Ukrainian scientists in the field of reliability theory [Streljnikov 2005] Should note that results in article were obtained for the first time thanks to using developed virtual (program) models of computer tools

Program models were used for calculating reliability parameters (eg time of no-failure operation) of portable device for express-diagnostic of plant state Floratest which is developed and created in the VM Glushkov Institute of Cybernetics of NAS of Ukraine

I T H E A

142

Conclusion

Presence of program unit for reliability parameters calculating as a part of VLCAD allows to fulfill prior calculating of reliability parameters of designed device and on the basis of obtained results make conclusion about correspondence of calculated parameters to beforehand specified ones Positive features of program unit is availability of two methods of reliability parameters calculating of separate microelectronic components and whole devices which are based on different models of distribution of failure probability (one- and two-parametric functions)

Program unit can be used not only for calculating of reliability parameters but in education process for gaining theoretical information from reliability theory

Program unit now is used in practical tasks for calculating reliability parameters of portable devices

Acknowledgements

This work is partially financed by Bulgarian National Science Fund under the joint Bulgarian-Ukrainian project D 002-331 19122008 Developing of Distributed Virtual Laboratories Based on Advanced Access Methods for Smart Sensor System Design as well as Ukrainian Ministry of Education under the joint Ukrainian-Bulgarian project No 145 23022009 with the same name

Bibliography

[Palagin 2009] Palagin O Romanov V Markov K Velychko V Stanchev P Galelyuka I Ivanova K Mitov I Developing of distributed virtual laboratories for smart sensor system design based on multi-dimensional access method Classification forecasting data mining International book series Information Science and Computing Number 8 Supplement to International Journal Information Technologies and Knowledge Volume 32009 ndash 2009 ndash P 155ndash161

[Romanov 2007] V Romanov V Fedak I Galelyuka Ye Sarakhan O Skrypnyk Portable Fluorometer for Express-Diagnostics of Photosynthesis Principles of Operation and Results of Experimental Researches Proceeding of the 4th IEEE Workshop on Intelligent Data Acquisition and Advanced Computing Systems Technology and Applications IDAACS2007 ndash Dortmund Germany ndash 2007 September 6ndash8 ndash Р 570ndash573

[Belyaev 1985] Belyaev Yu Bogatyryov V Bolotin V et al Reliability of technical systems reference book Editor Ushakov I ndash Moskow 1985 ndash 608 p (in Russian)

[MIL-STD-883] MIL-STD-883 Test Methods and Procedures for Microcircuits

[Azarskov 2004] Azarskov V Streljnikov V Reliability of control and automation systems tutorial ndash Kiev 2004 ndash 164 p

[Streljnikov 2004] Streljnikov V Estimating of life of products of electronic techniques Mathematical machines and systems ndash 2004 ndash 2 ndash P 186ndash195

[ADI 2004] ADI reliability handbook ndash Norwood Analog Devices Inc 2004 ndash 86 с

[Motorola 1996] Reliability and quality report Fourth quarter 1996 ndash Motorola Inc 1996

[Romanov 2003] Romanov V quantitative estimation of reliability of integrated circuits by results of accelerated tests Electronic components and systems ndash 2003 ndash 10 ndash P 3ndash6

[Streljnikov 2002] Streljnikov V Feduhin A Estimation and prognostication of reliability of electronic elements and systems ndash Kiev Logos 2002 ndash 486 p

[Streljnikov 2005] Streljnikov V Method errors of calculating of reliably of systems Systemic problems of reliability quality information and electronic technologies 10-th international conference Conference works ndash October 2005 ndash Sochi Russia ndash Part 6ndash P 136ndash143


143

Authors Information

Oleksandr Palagin ndash Academician of National Academy of Sciences of Ukraine Depute-director of VM Glushkovrsquos Institute of Cybernetics of National Academy of Sciences of Ukraine Doctor of technical sciences professor Prospect Akademika Glushkova 40 Kievndash187 03680 Ukraine e-mail palagin_aukrnet

Peter Stanchev ndash Professor Kettering University Flint MI 48504 USA Institute of Mathematics and Informatics ndash BAS Acad GBontchev St bl8 Sofia-1113 Bulgaria e-mail pstancheketteringedu

Volodymyr Romanov ndash Head of department of VM Glushkovrsquos Institute of Cybernetics of National Academy of Sciences of Ukraine Doctor of technical sciences professor Prospect Akademika Glushkova 40 Kievndash187 03680 Ukraine e-mail dept230insygkievua VRomanoviua

Krassimir Markov ndash Institute of Mathematics and Informatics BAS Acad GBonthev St bl8 Sofia-1113 Bulgaria e-mail markovfoibgcom

Igor Galelyuka ndash Senior research fellow of VM Glushkovrsquos Institute of Cybernetics of National Academy of Sciences of Ukraine Candidate of technical science Prospect Akademika Glushkova 40 Kievndash187 03680 Ukraine e-mail galibgalanet

Vitalii Velychko ndash Doctoral Candidate VMGlushkov Institute of Cybernetics of NAS of Ukraine Prosp Akad Glushkov 40 Kiev-03680 Ukraine e-mail velychkoaduiscomua

Oleksandra Kovyriova ndash research fellow of VM Glushkovrsquos Institute of Cybernetics of National Academy of Sciences of Ukraine Prospect Akademika Glushkova 40 Kievndash187 03680 Ukraine e-mail alexandaraskripkagmailcom

Oksana Galelyuka ndash Research fellow of Institute of encyclopedic researches of National Academy of Sciences of Ukraine Tereschenkivska str 3 Kiev 01004 Ukraine

Ilia Mitov ndash Institute of Information Theories and Applications FOI ITHEA PO Box 775 Sofia-1090 Bulgaria e-mail mitovfoibgcom

Krassimira Ivanova ndash Researcher Institute of Mathematics and Informatics BAS Acad GBonthev St bl8 Sofia-1113 Bulgaria e-mail ivanovafoibgcom

IBS-18-2010-New_Trends_in_iTECH-final 1


2

Krassimir Markov Vitalii Velychko Lius Fernando de Mingo Lopez Juan Casellanos (ed)


ITHEAreg

Sofia Bulgaria 2010

ISBN 978-954-16-0044-9

First edition

Recommended for publication by The Scientific Concil of the Institute of Information Theories and Applications FOI ITHEA

This book maintains articles on actual problems of research and application of information technologies especially the new approaches models algorithms and methods of membrane computing and transition P systems decision support systems discrete mathematics problems of the interdisciplinary knowledge domain including informatics computer science control theory and IT applications information security disaster risk assessment based on heterogeneous information (from satellites and in-situ data and modelling data) timely and reliable detection estimation and forecast of risk factors and on this basis on timely elimination of the causes of abnormal situations before failures and other undesirable consequences occur models of mind cognizers computer virtual reality virtual laboratories for computer-aided design open social info-educational platforms multimedia digital libraries and digital collections representing the European cultural and historical heritage recognition of the similarities in architectures and power profiles of different types of arrays adaptation of methods developed for one on others and component sharing when several arrays are embedded in the same system and mutually operated It is represented that book articles will be interesting for experts in the field of information technologies as well as for practical users

General Sponsor Consortium FOI Bulgaria (wwwfoibgcom)

Printed in Bulgaria

Copyright copy 2010 All rights reserved

copy 2010 ITHEAreg ndash Publisher Sofia 1000 POB 775 Bulgaria wwwitheaorg e-mail infofoibgcom

copy 2010 Krassimir Markov Vitalii Velychko Lius Fernando de Mingo Lopez Juan Casellanos ndash Editors

copy 2010 Ina Markova ndash Technical editor

copy 2010 For all authors in the book

reg ITHEA is a registered trade mark of FOI-COMMERCE Co

ISBN 978-954-16-0044-9

Co Jusautor Sofia 2010

I T H E A

134







Introduction







135








I T H E A

136


















2

2

AtHN

(1)



137


11

rv TTk

Ea

eAt (2)



1

0 T (3)


1

1

n

jjj

еср mT (4)




N

EDHtн (5)


AtHNEDH (6)


)(

)(

н

н

tR

tf (7)

where

2

exp2

)(0

200

н

н

ннн tT

Tt

tt

Ttf

(8)

)2exp()(0

0

0

0

н

н

н

нн

tT

TtФ

tT

tTФtR (9)


2exp

2 0

200

н

н

нн tT

Tt

tt

T

(10)


I T H E A

138

2

1

1

2

n

jjj

Dср TmT (11)





139



I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2

I T H E A

134







Introduction







135








I T H E A

136


















2

2

AtHN

(1)



137


11

rv TTk

Ea

eAt (2)



1

0 T (3)


1

1

n

jjj

еср mT (4)




N

EDHtн (5)


AtHNEDH (6)


)(

)(

н

н

tR

tf (7)

where

2

exp2

)(0

200

н

н

ннн tT

Tt

tt

Ttf

(8)

)2exp()(0

0

0

0

н

н

н

нн

tT

TtФ

tT

tTФtR (9)


2exp

2 0

200

н

н

нн tT

Tt

tt

T

(10)


I T H E A

138

2

1

1

2

n

jjj

Dср TmT (11)





139



I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2


135








I T H E A

136


















2

2

AtHN

(1)



137


11

rv TTk

Ea

eAt (2)



1

0 T (3)


1

1

n

jjj

еср mT (4)




N

EDHtн (5)


AtHNEDH (6)


)(

)(

н

н

tR

tf (7)

where

2

exp2

)(0

200

н

н

ннн tT

Tt

tt

Ttf

(8)

)2exp()(0

0

0

0

н

н

н

нн

tT

TtФ

tT

tTФtR (9)


2exp

2 0

200

н

н

нн tT

Tt

tt

T

(10)


I T H E A

138

2

1

1

2

n

jjj

Dср TmT (11)





139



I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2

I T H E A

136


















2

2

AtHN

(1)



137


11

rv TTk

Ea

eAt (2)



1

0 T (3)


1

1

n

jjj

еср mT (4)




N

EDHtн (5)


AtHNEDH (6)


)(

)(

н

н

tR

tf (7)

where

2

exp2

)(0

200

н

н

ннн tT

Tt

tt

Ttf

(8)

)2exp()(0

0

0

0

н

н

н

нн

tT

TtФ

tT

tTФtR (9)


2exp

2 0

200

н

н

нн tT

Tt

tt

T

(10)


I T H E A

138

2

1

1

2

n

jjj

Dср TmT (11)





139



I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2


137


11

rv TTk

Ea

eAt (2)



1

0 T (3)


1

1

n

jjj

еср mT (4)




N

EDHtн (5)


AtHNEDH (6)


)(

)(

н

н

tR

tf (7)

where

2

exp2

)(0

200

н

н

ннн tT

Tt

tt

Ttf

(8)

)2exp()(0

0

0

0

н

н

н

нн

tT

TtФ

tT

tTФtR (9)


2exp

2 0

200

н

н

нн tT

Tt

tt

T

(10)


I T H E A

138

2

1

1

2

n

jjj

Dср TmT (11)





139



I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2

I T H E A

138

2

1

1

2

n

jjj

Dср TmT (11)





139



I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2


139



I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2

I T H E A

140






CB = 60 CB = 90 CB = 60 CB = 90

1 000 hours

years

629723

71886

320256

36559

82298

9395

76647

8749

20 000 hours

years

31486

3594

16372

1869

18402

2101

17139

1956

50 000 hours

years

12594

1438

6549

0748

11639

1329

10840

1237

100 000 hours

years

6297

0719

3274

0373

8230

0939

7665

0875

200 000 hours

years

3149

0359

1637

0187

5819

0664

5420

0619


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2


141







I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2

I T H E A

142

Conclusion




Acknowledgements


Bibliography













143

Authors Information













2


143

Authors Information













2

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